ON ELLIPTIC EQUATIONS WITH SINGULAR POTENTIALS AND NONLINEAR BOUNDARY CONDITIONS

Autor(es)

Ferreira, Lucas C. F. ^[1] ; Neves, Sergio L. N. ^[2]

Afiliação do(s) autor(es)

^[1] Univ Estadual Campinas, Dept Math, BR-13083859 Campinas, SP - Brazil

^[2] UNESP, Ibilce, Dept Math, BR-15054000 Sao Jose Do Rio Preto, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: QUARTERLY OF APPLIED MATHEMATICS; v. 76, n. 4, p. 699-711, DEC 2018.
• Citações Web of Science: 0

Resumo

We consider the Laplace equation in the half-space satisfying a nonlinear Neumann condition with boundary potential. This class of problems appears in a number of mathematical and physics contexts and is linked to fractional dissipation problems. Here the boundary potential and nonlinearity are singular and of power-type, respectively. Depending on the degree of singularity of potentials, first we show a nonexistence result of positive solutions in D-1,D-2(R-+(n)) with a L-p-type integrability condition on partial derivative R-+(n). After, considering critical nonlinearities and conditions on the size and sign of potentials, we obtain the existence of positive solutions by means of minimization techniques and perturbation methods. (AU)

• Processo FAPESP: 12/10153-6 - Equações Elípticas não-lineares com Potenciais Singulares
• Beneficiário: Sérgio Leandro Nascimento Neves
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado